A composite number

is a optimistic integer
1" /> i beg your pardon is not prime (i.e., i beg your pardon has factors other 보다 1 and also itself). The first couple of composite number (sometimes dubbed "composites" for short) are 4, 6, 8, 9, 10, 12, 14, 15, 16, ... (OEIS A002808), who prime decompositions are summarized in the adhering to table. Note that the number 1 is a special case which is considered to be neither composite nor prime.

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 prime factorization prime factorization 4 20 6 21 8 22 9 24 10 25 12 26 14 27 15 28 16 30 18 32

The

th composite number
have the right to be generated using the benidormclubdeportivo.org Language code

Composite := FixedPoint + 1&, n>The Dirichlet generating function of the characteristic duty of the composite numbers

is provided by

 )/(n^s)" /> (1) (2) (3)

where

is the Riemann zeta function,
is the element zeta function, and also
" /> is an Iverson bracket.

There room an infinite variety of composite numbers.

The composite number problem asks if there exist positive integers

and also
such that
.

A composite number

can constantly be created as a product in at least two ways (since
is always possible). Call these 2 products

(4)

then it is clear the situation that

(
divides
). Set

(5)

where

is the component of
which divides
, and also
is the component of
i m sorry divides
. Climate there room
and also
together that

 (6) (7)

Solving

for
gives

(8)

 (9)(10)(11)

It as such follows the

is never prime! In fact, the much more general result that

(12)

is never prime for

an essence
=0" /> likewise holds (Honsberger 1991).

SEE ALSO: Amenable Number, Composite Number Problem, Grimm"s Conjecture, very Composite Number, prime Factorization prime Gaps, element Number, Weakly Prime
REFERENCES:

Honsberger, R. Much more Mathematical Morsels. Washington, DC: Math. Assoc. Amer., pp.19-20, 1991.

Sloane, N.J.A. Sequence A002808/M3272in "The On-Line Encyclopedia of integer Sequences."

Referenced ~ above benidormclubdeportivo.org|Alpha: Composite Number
CITE THIS AS:

Weisstein, Eric W. "Composite Number."From benidormclubdeportivo.org--A benidormclubdeportivo.org web Resource. Https://benidormclubdeportivo.org/CompositeNumber.html

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